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Jan 15, 2021 at 4:48 comment added Mohammad Golshani @AndrésE.Caicedo At least not visible. To show the existence of generic filter, we just count dense sets and build the filter inductively. To show the generic filter is not in the ground model, we just use the fact that its complement is dense.
Jan 14, 2021 at 17:20 comment added Andrés E. Caicedo This is cute, but likely diagonalization is recognizable arguing that generics exist and don't belong to the ground model.
Jan 14, 2021 at 9:32 comment added Asaf Karagila The problem here is that we use such heavy machinery that it's not clear if we used the uncountability of the reals somewhere in the process. If we did, the proof is circular.
Jan 14, 2021 at 9:28 history edited Mohammad Golshani CC BY-SA 4.0
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Jan 14, 2021 at 9:26 history edited Martin Sleziak CC BY-SA 4.0
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Jan 14, 2021 at 9:19 history answered Mohammad Golshani CC BY-SA 4.0